Shikaku Rules: How to Play, Strategies and Variations

What is Shikaku?

Shikaku is a grid-dividing puzzle. You start with a square or rectangular grid in which some cells hold numbers. Your job is to cut the whole grid into rectangles (squares count too) so that every rectangle contains exactly one number, and that number equals the rectangle's area, the count of cells inside it.

A 6 might become a 1×6 strip, a 2×3 block or a 3×2 block. A 4 might be a 1×4 line, a 4×1 line or a 2×2 square. Each piece has to fit around its neighbors with no gaps and no overlaps, and that is where the logic comes from.

Because the rule is so short and the arithmetic so gentle, Shikaku is one of the best first puzzles for newcomers to logic grids. It sits in the same family as Nurikabe, where numbers also describe the size of areas, but Shikaku keeps every shape a tidy rectangle and asks you to cover every single cell.

A short history

Shikaku is an original puzzle of the Japanese publisher Nikoli, the company that also gave Sudoku its name and popularized it worldwide. The full Japanese title is Shikaku ni Kire, roughly "divide by squares", and Nikoli's English materials call it Divide by Box. Other collections publish it simply as Rectangles.

Nikoli describes Shikaku as a puzzle with a very simple rule that still rewards real reasoning, and points out that it doubles as multiplication practice for children: a 12 might be 1×12, 2×6 or 3×4.

Mathematicians have studied it too. The general problem of deciding whether a Shikaku grid can be solved has been proven NP-complete, which puts it alongside many other famous pencil puzzles. You can read more in Wikipedia's Shikaku article.

The core rules

A standard Shikaku follows four rules. They are short enough to memorize in one read.

1. 1Divide the grid into rectanglesDraw lines along the grid lines to split the whole board into rectangles. A square is a rectangle too, and so is a single row or column of cells.
2. 2One number per rectangleEvery rectangle contains exactly one number. A rectangle with no number, or with two numbers, breaks the rules.
3. 3The number is the areaThe number inside a rectangle tells you how many cells that rectangle covers. A 6 covers six cells, a 2 covers two.
4. 4Cover every cellThe rectangles tile the grid completely, with no overlaps and no leftover cells. Every cell belongs to exactly one rectangle.

A quick consequence: the numbers in a correct puzzle always add up to the total number of cells. In a 6×6 grid they sum to 36, which is a handy way to check a puzzle you have copied by hand.

A solved example

Here is a 6×6 Shikaku with nine numbers. It has exactly one solution. Try it yourself before looking at the colored rectangles on the right.

Start in the corners. The 8 in the bottom-left corner cannot be a 1×8 line because the grid is only six cells wide, and a 4×2 block running up the left side would swallow the 6. So it must be the 2×4 block along the bottom two rows. Next, the 2 in the second row of the right-hand column has a 3 to its left and another 2 below it, so it can only pair with the corner cell above it. Now look at the bottom-right corner: only the 2 just above it can reach it, so that 2 runs downward, and the cell to its left can then be covered only by the 3 above it, which becomes a vertical strip. The remaining 3, the 4 and the two 6s then fit together in only one way.

How to play: a step-by-step method

This routine works on any Shikaku, and on small grids it usually carries you all the way to the answer.

1. List the shapes for each number. Write down the factor pairs. A 2 is 1×2, a 6 is 1×6 or 2×3, an 8 is 1×8 or 2×4, each in either orientation.
2. Rule out shapes that do not fit. A shape is impossible if it runs off the edge or swallows a second number. Large numbers near edges often lose most of their options at once.
3. Lock in any number with one placement left. Draw its rectangle firmly. Every rectangle you place removes cells from the options of its neighbors.
4. Look for cells only one number can reach. Pick an empty cell, often a corner, and ask which numbers could stretch to cover it. If only one can, that number's rectangle must include it.
5. Shade or mark finished areas. Lightly coloring each completed rectangle makes the remaining gaps easy to see, and gaps are where the next deduction usually hides.
6. Repeat until the grid is full. Each placement opens up the next. If you stall, return to step 4 and check every uncovered cell again.

Strategies experienced solvers use

Shikaku rewards a few simple habits. Once they become automatic, even 10×10 grids go quickly.

The heart of Shikaku is switching between two questions: where can this number go, and which number can reach this cell? If you like that kind of area logic, Nurikabe and Star Battle use it in different ways. For steady practice, LogicPuzzles.io has free Shikaku rectangle puzzles with a new daily grid and unlimited 6×6, 8×8 and 10×10 boards.

Popular variations and relatives

Classic Shikaku is the version you will meet most often, but a few close cousins use the same idea of dividing a grid by clues.

• Bigger and rectangular grids. Puzzles range from tiny 5×5 starters to large boards with dozens of clues. The rules never change, only the amount of searching.
• Fillomino. Another Nikoli grid-dividing puzzle. The pieces can be any shape, every cell gets a number equal to its piece's size, and pieces of the same size may not touch along an edge.
• Sashigane. A Nikoli relative in which the grid is cut into L-shaped pieces, with clues marking the corners and ends of each L.
• Arithmetic cousins. KenKen and Killer Sudoku also hand you regions with numbers, but there the regions are given and you fill in digits instead of drawing the shapes.

Common mistakes

The most common slip is forgetting an orientation. A 2×3 block can also stand as a 3×2 block, and a 1×4 line can run across or down. Always check both before you decide a number is stuck.

Second, beginners often place the first shape that fits. Shikaku has one correct answer, so a rectangle should only be drawn when it is the only option, not just a possible one. Guessing early tends to leave an awkward hole later.

Third, watch for rectangles that quietly swallow a second number. It is easy to stretch a 6 across a row and miss a small 2 tucked inside it.

Finally, remember that every cell must be covered. A finished-looking grid with one stray empty cell means at least one rectangle is in the wrong place.

What makes a Shikaku hard?

Easy Shikaku grids have many small numbers and plenty of primes, so most pieces are forced at a glance. Harder grids use larger composite numbers such as 12, 16 or 24, which have many possible shapes, and space the clues so that no corner or edge gives itself away immediately.

On those grids, the orphan-cell question becomes the main tool: instead of asking where each number goes, you look for the cells that only one number can possibly reach. That shift in perspective is the step from beginner to confident solver.

Frequently asked questions